$\begin{cases}b(1)=-54\\\\ b(n)=b(n-1)\cdot \dfrac{4}{3} \end{cases}$ What is the $4^{\text{th}}$ term in the sequence?
Explanation: This is a recursive formula. It tells us that the first term is $-54$ and that the common ratio is $\dfrac{4}{3}$. $\begin{aligned} {b(1)}&=-54 \\\\ {b(2)}&={b(1)}\cdot \dfrac{4}{3}=-72 \\\\ {b(3)}&={b(2)}\cdot \dfrac{4}{3}=-96 \\\\ {b(4)}&={b(3)}\cdot \dfrac{4}{3}=-128 \end{aligned}$ The $4^{\text{th}}$ term is $-128$.